A tensegrity is a stable discrete structure made from stiff bars or strutsA strut is a rod-shaped material which can stretch but cannot shrink. connected by cables with tension. See Figure REF .
Since its invention by American sculptor Kenneth Snelson, a tensegrity has attracted wide attention not only in structural engineering but also in mathematics, see, e.g., [1]}.
One of the challenges in the study of tensegrities is to understand the impact of the combinatorics underlying stable tensegrities.
The aim of this paper is to relate such a combinatorial question in the tensegrity analysis to a topic in spectral graph theory and derive combinatorial characterizations of the graphs of stable tensegrities.
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